Striking examples of episodic activity in active galactic nuclei are the double-double radio galaxies (DDRGs) with two pairs of oppositely-directed radio lobes from two different cycles of activity. Although there are over about a dozen good examples of DDRGs, so far no case of one associated with a quasar has been reported. We present Giant Metrewave Radio Telescope observations of a candidate double-double radio quasar (DDRQ), J0935+0204 (4C02.27), and suggest that radio jets in this source may also have been intrinsically asymmetric, contributing to the large observed asymmetries in the flux density and location of both pairs of radio lobes.